{"id":1975,"date":"2025-03-03T15:16:41","date_gmt":"2025-03-03T15:16:41","guid":{"rendered":"https:\/\/cful.letras.ulisboa.pt\/lancog\/?p=1975"},"modified":"2026-02-05T14:36:56","modified_gmt":"2026-02-05T14:36:56","slug":"seminar-series-in-analytic-philosophy-2024-25-session-16","status":"publish","type":"post","link":"https:\/\/cful.demiurgos.eu\/lancog\/seminar-series-in-analytic-philosophy-2024-25-session-16\/","title":{"rendered":"Seminar Series in Analytic Philosophy 2024-25: Session 16"},"content":{"rendered":"<p style=\"font-weight: 400;\"><strong>Higher-Order Metaphysical Resolutions of the Continuum Hypothesis<\/strong><\/p>\n<p style=\"font-weight: 400;\">Peter Fritz (University College London)<\/p>\n<p>&nbsp;<\/p>\n<p style=\"font-weight: 400;\">7 March 2025, 16:00 (Lisbon Time \u2013 WET)<\/p>\n<p style=\"font-weight: 400;\">Faculdade de Letras de Lisboa<\/p>\n<p style=\"font-weight: 400;\">Sala Mattos Rom\u00e3o [C201.J] (Departamento de Filosofia)<\/p>\n<p>&nbsp;<\/p>\n<p style=\"font-weight: 400;\"><strong>Abstract:<\/strong>\u00a0I aim to draw a connection between higher-order metaphysics and the philosophy of mathematics, in particular set theory. Higher-order metaphysics means carrying out metaphysical debates in higher-order logic, using higher-order quantifiers to regiment talk of propositions, properties, and relations. A prominent topic in this area is grain science, the investigation of individuation conditions of propositions, properties, and relations. These topics seem purely metaphysical. But I will argue that they are intimately connected to questions in (the philosophy of) mathematics. In particular, I will argue that views about grain science can resolve the continuum hypothesis. To do so, I will present an example of such a view. I won&#8217;t argue for it, but I hope to motivate, first, that the view is attractive, or at least not implausible; second, that the view doesn&#8217;t obviously prejudge controversial questions in (the philosophy of) set theory; and third, that the view nevertheless settles the continuum hypothesis. The view assumes that sets obey the principles of ZFC set theory, and that propositions form a structure which corresponds to a particular complete Boolean algebra. Adapting standard forcing results using Boolean-valued models, we can show that this higher-order metaphysical view entails the failure of the continuum hypothesis.<\/p>\n<p>&nbsp;<\/p>\n<p>This work\/event is funded by Portuguese national funds through FCT &#8211; Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia, I.P., within the project UID\/00310\/2025, Centro de Filosofia da Universidade de Lisboa<br \/>\n(https:\/\/doi.org\/10.54499\/UID\/00310\/2025)<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Higher-Order Metaphysical Resolutions of the Continuum Hypothesis Peter Fritz (University College London) &nbsp; 7 March 2025, 16:00 (Lisbon Time \u2013 WET) Faculdade de Letras de Lisboa Sala Mattos Rom\u00e3o [C201.J] (Departamento de Filosofia) &nbsp; Abstract:\u00a0I aim to draw a connection between higher-order metaphysics and the philosophy of mathematics, in particular set theory. Higher-order metaphysics means [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"activitypub_content_warning":"","activitypub_content_visibility":"","activitypub_max_image_attachments":4,"activitypub_interaction_policy_quote":"anyone","activitypub_status":"federate","footnotes":""},"categories":[1],"tags":[],"class_list":["post-1975","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/cful.demiurgos.eu\/lancog\/wp-json\/wp\/v2\/posts\/1975","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/cful.demiurgos.eu\/lancog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/cful.demiurgos.eu\/lancog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/cful.demiurgos.eu\/lancog\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/cful.demiurgos.eu\/lancog\/wp-json\/wp\/v2\/comments?post=1975"}],"version-history":[{"count":1,"href":"https:\/\/cful.demiurgos.eu\/lancog\/wp-json\/wp\/v2\/posts\/1975\/revisions"}],"predecessor-version":[{"id":2134,"href":"https:\/\/cful.demiurgos.eu\/lancog\/wp-json\/wp\/v2\/posts\/1975\/revisions\/2134"}],"wp:attachment":[{"href":"https:\/\/cful.demiurgos.eu\/lancog\/wp-json\/wp\/v2\/media?parent=1975"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/cful.demiurgos.eu\/lancog\/wp-json\/wp\/v2\/categories?post=1975"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/cful.demiurgos.eu\/lancog\/wp-json\/wp\/v2\/tags?post=1975"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}